Differential Quadrature and Differential Quadrature Based Element Methods - 1st Edition - ISBN: 9780128030813, 9780128031070

Differential Quadrature and Differential Quadrature Based Element Methods

1st Edition

Theory and Applications

Authors: Xinwei Wang
eBook ISBN: 9780128031070
Paperback ISBN: 9780128030813
Imprint: Butterworth-Heinemann
Published Date: 25th March 2015
Page Count: 408
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Description

Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications is a comprehensive guide to these methods and their various applications in recent years. Due to the attractive features of rapid convergence, high accuracy, and computational efficiency, the differential quadrature method and its based element methods are increasingly being used to study problems in the area of structural mechanics, such as static, buckling and vibration problems of composite structures and functional material structures.


This book covers new developments and their applications in detail, with accompanying FORTRAN and MATLAB programs to help you overcome difficult programming challenges. It summarises the variety of different quadrature formulations that can be found by varying the degree of polynomials, the treatment of boundary conditions and employing regular or irregular grid points, to help you choose the correct method for solving practical problems.

Key Features

  • Offers a clear explanation of both the theory and many applications of DQM to structural  analyses
  • Discusses and illustrates reliable ways to apply multiple boundary conditions and develop reliable grid distributions
  • Supported by FORTRAN and MATLAB programs, including subroutines to compute grid distributions and weighting coefficients

Readership

Structural engineers, computational engineers, practicing engineers, graduate students majoring in engineering, researchers in transport processes, fluid mechanics, static and dynamic structural mechanics, static aero-elasticity, and lubrication mechanics.

Table of Contents

  • Preface
  • Acknowledgments
  • Chapter 1: Differential Quadrature Method
    • Abstract
    • 1.1. Introduction
    • 1.2. Integral quadrature
    • 1.3. Differential quadrature method
    • 1.4. Determination of weighting coefficients
    • 1.5. Explicit formulation of weighting coefficients
    • 1.6. Various grid points
    • 1.7. Error analysis
    • 1.8. Local adaptive differential quadrature method
    • 1.9. Differential quadrature time integration scheme
    • 1.10. Summary
  • Chapter 2: Differential Quadrature Element Method
    • Abstract
    • 2.1. Introduction
    • 2.2. Differential quadrature element method
    • 2.3. DQEM with Hermite interpolation
    • 2.4. DQEM with Lagrange interpolation
    • 2.5. Assemblage procedures
    • 2.6. Discussion
    • 2.7. Summary
  • Chapter 3: Methods of Applying Boundary Conditions
    • Abstract
    • 3.1. Introduction
    • 3.2. Basic equations of a Bernoulli–Euler beam
    • 3.3. Methods for applying multiple boundary conditions
    • 3.4. Discussion
    • 3.5. Numerical examples
    • 3.6. Summary
  • Chapter 4: Quadrature Element Method
    • Abstract
    • 4.1. Introduction
    • 4.2. Quadrature element method
    • 4.3. Quadrature bar element
    • 4.4. Quadrature Timoshenko beam element
    • 4.5. Quadrature plane stress (strain) element
    • 4.6. Quadrature thick plate element
    • 4.7. Quadrature thin beam element
    • 4.8. Quadrature thin rectangular plate element
    • 4.9. Extension to quadrilateral plate element with curved edges
    • 4.10. Discussion
    • 4.11. Summary
  • Chapter 5: In-plane Stress Analysis
    • Abstract
    • 5.1. Introduction
    • 5.2. Formulation-I
    • 5.3. Formulation-II
    • 5.4. Results and discussion
    • 5.5. Equivalent boundary conditions
    • 5.6. Summary
  • Chapter 6: Static Analysis of Thin Plate
    • Abstract
    • 6.1. Introduction
    • 6.2. Rectangular thin plate under general loading
    • 6.2.3. Equivalent load
    • 6.3. Applications
    • 6.4. Summary
  • Chapter 7: Linear Buckling Analysis of Thin Plate
    • Abstract
    • 7.1. Introduction
    • 7.2. Buckling of rectangular thin plate
    • 7.3. Applications
    • 7.4. Summary
  • Chapter 8: Free Vibration Analysis of Thin Plate
    • Abstract
    • 8.1. Introduction
    • 8.2. Free vibration of rectangular thin plate
    • 8.3. Examples
    • 8.4. Summary
  • Chapter 9: Geometric Nonlinear Analysis
    • Abstract
    • 9.1. Introduction
    • 9.2. Nonlinear stability of thin doubly curved orthotropic shallow shell
    • 9.3. Buckling of inclined circular cylinder-in-cylinder
    • 9.4. Buckling and postbuckling analysis of extensible beam
    • 9.5. Summary
  • Chapter 10: Elastoplastic Buckling Analysis of Plate
    • Abstract
    • 10.1. Introduction
    • 10.2. Elastoplastic buckling of thin rectangular plate
    • 10.3. Elastoplastic buckling of thick rectangular plate
    • 10.4. Summary
  • Chapter 11: Structural Analysis by the QEM
    • Abstract
    • 11.1. Introduction
    • 11.2. Dynamic analysis of a flexible rod Hit by rigid ball
    • 11.3. Free vibration of thin plates
    • 11.4. Buckling of thin rectangular plate
    • 11.5. Summary
  • Appendix I
  • Appendix II
  • Appendix III
  • Appendix IV
  • Appendix V
  • Appendix VI
  • Appendix VII
  • Appendix VIII
  • Appendix IX
  • Index

Details

No. of pages:
408
Language:
English
Copyright:
© Butterworth-Heinemann 2015
Published:
Imprint:
Butterworth-Heinemann
eBook ISBN:
9780128031070
Paperback ISBN:
9780128030813

About the Author

Xinwei Wang

Professor at Nanjing University of Aeronautics and Astronautics in China since 1993, Dr. Wang earned his MS degree in solid mechanics from the same university, and his PhD in mechanical engineering from the University of Oklahoma, USA. Prof. Wang has been a visiting scholar at the University of Michigan at Dearborn, the University of Maryland at Baltimore County, the University of Oklahoma and the University of California at Los Angeles. He has published over 200 papers in the areas of numerical methods and computational engineering, mechanics of composite materials and experimental finite plasticity, with over 50 of these related to the differential quadrature method.

Affiliations and Expertise

Nanjing University of Aeronautics and Astronautics, China.

Reviews

"...explores the applications of the differential quadrature method (DQM) to problems of structural mechanics, including static stress analysis, buckling analysis and vibration and dynamic analysis. Linear, geometrically nonlinear, and material nonlinear problems are involved." --Zentralblatt MATH

Ratings and Reviews